Interim Schools Chancellor Harold Levy is getting an A from many observers during his brief stint — and talk is mounting that he should be hired full-time if he wants the job.

The Board of Education has launched a $160,000 national search for a “permanent” chancellor to replace Levy — a Citigroup executive who, over the objections of Mayor Giuliani, was given a six-month contract to hold the fort.

Levy has declined to comment on his long-term plans. But he’s made clear he wants to do as much as he can while he’s in charge, and insiders say he doesn’t want to be tagged as a lame duck before he leaves.

Here’s what Levy has done during his first six weeks:

Established written guidelines to evaluate the performance of superintendents.

Threatened to fire the chief janitor at 110 Livington St. — board headquarters — for letting the building become an “absolute pigsty” and attacked his nearly $100,000 annual pay as “outrageously high.” The building is much cleaner now.

Sent e-mail messages to all superintendents and principals asking for their recommendations for reforms.

Ordered a streamlining of paper-intensive school regulations, and abolished a rule that prevented personnel files from following teachers transferring from one school to another. Principals had complained that they didn’t know if they were getting bad apples.

Initiated an overhaul of the disciplinary process for teachers charged with wrongdoing, and vowed to negotiate changes in the union contract to make it easier to get rid of bad teachers.

Tried to break the ice with City Hall by considering hiring former Deputy Mayor Randy Levine, a labor lawyer and Giuliani favorite, to help negotiate a new teachers contract.

Vowed to personally scrutinize school-construction projects. He has requested copies of all construction-related complaints filed by principals with the School Construction Authority, and more specifics on why projects are delayed.

A Levy bid to stay on would still be a tough sell because Giuliani — who has three committed votes on the seven-member Board of Ed — is dead-set against him. The mayor has refused even to meet with him.

“The plan has always been to hire an interim chancellor who would serve as a bridge and then hire a different full-time chancellor,” said Deputy Mayor Tony Coles.

He also said the mayor is still suspicious that Levy is too cozy with the United Federation of Teachers, which backed his candidacy.

But the board defied the mayor once and could do so again.

Queens board member Terri Thomson — who cast the swing vote to hire Levy — said she would not rule out any possibility in the chancellor search.

“It’s too early to have those discussions. It’s very early in the search process,” she said.

But Thomson said Levy is doing a “terrific job.” He has a “fresh eye” for spotting problems, and attacks them, she added.

Other prominent officials — including those vying to succeed Giuliani — echoed those sentiments.

“It would be odd to consider qualified people throughout the country — except the person who happens to be the chancellor and is doing a good job of it,” said Public Advocate Mark Green.

Bronx Borough President Fernando Ferrer gave Levy an A for action, and said he should be a “top” candidate for permanent chancellor — if he’s interested.

“I am very favorably impressed. He ought to be considered a leading candidate. He already has shown me he definitely deserves more time,” said Ferrer, who appoints one of the seven board members.

And business leaders like what they see.

“Levy seems to be doing what the mayor wants the chancellor to do — clean house,” saw Lewis Rudin, president of the Association for a Better New York, and a friend of Levy.

Levy has garnered wide praise from the media’s opinion writers, with the New York Observer urging the board to keep him.

But some supporters have been told that Levy won’t stay beyond his contract.

“As an interim chancellor he can rock the boat. We think he should rock the boat as much as he can,” she said.

She said Manhattan board member Irving Hamer — a Levy supporter — told her Levy wanted to return to his senior vice president job at Citigroup.

Levy has long been interested in education. Before taking the chancellor’s post, he was a member of the state Board of Regents. In 1995, he issued a blistering report about the city’s shoddy school maintenance and the lack of funds to deal with it.